Biblatex-apa: No change of citation with three authors to "et al." ("/u.a." in german) after first citing the source

This is, in fact, the correct disambiguation behaviour. When you cite the 2004 paper, the biblatex "uniquelist" feature (which APA requires) expands the name lists to the point of minimum ambiguity which is:

Stroebe & Nijstad et al.
Strobe & Nijstad

However, since "et al" is plural and should not replace only one name, the hidden name is printed instead of "et al". I have confirmed this as correct behaviour with the APA and it will appear in future revisions of the official style.

set maxcitenames

\usepackage[backend=biber,style=apa,babel=other,maxcitenames=3]{biblatex}